Problem: Simplify the following expression: $ z = \dfrac{7}{p - 10} - \dfrac{-5}{8} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8}{8}$ $ \dfrac{7}{p - 10} \times \dfrac{8}{8} = \dfrac{56}{8p - 80} $ Multiply the second expression by $\dfrac{p - 10}{p - 10}$ $ \dfrac{-5}{8} \times \dfrac{p - 10}{p - 10} = \dfrac{-5p + 50}{8p - 80} $ Therefore $ z = \dfrac{56}{8p - 80} - \dfrac{-5p + 50}{8p - 80} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{56 - (-5p + 50) }{8p - 80} $ Distribute the negative sign: $z = \dfrac{56 + 5p - 50}{8p - 80}$ $z = \dfrac{5p + 6}{8p - 80}$